Consistent EKF-Based Visual-Inertial Navigation Using Points and Lines

In this paper, we present a novel visual-inertial navigation system (VINS) algorithm using points and lines for low cost and computationally constrained systems in GPS-denied environments. Generally, extended Kalman filter (EKF)-based VINS algorithms exploit points as visual information and suffer from an inconsistent state estimates resulting in obtaining spurious information along the unobservable direction, especially along the rotation about the gravity direction. While point features are simple and rich visual information, line features are alternative visual information in low-texture environments, such as indoors or urban areas. To improve the robustness and consistency, we simultaneously exploit the points and lines as visual information for the VINS algorithm and model the state space as a matrix Lie group, based on the theory of the invariant EKF. In particular, as the main theoretical contributions of this paper, we employ the line observations to the VINS algorithm on the matrix Lie group and analytically derive the right null space of the corresponding observability matrix for the first time. By leveraging this analysis, we prove that it has a consistent property for the rotation about the gravity direction without any artificial remedies. Therefore, the proposed VINS algorithm on the matrix Lie group using points and lines naturally enforces the state vector to remain in the unobservable subspace. The performance of the proposed method is validated through Monte-Carlo simulations and real-world experiments.